Greatest common divider calculator

Enter the two numbers whose gcd is to be calculated and then click on "Calculate".

Greatest common divider - What does it mean?

The greatest common divider (gcd) is a term in mathematics. It is the largest natural number by which two integers can be divided without remainder. The gcd is at least 1 and at most the smaller of the two numbers. If the gcd is 1, then one calls both numbers divider-alien. The gcd is mainly used in fractions, but also in number theory.
In fraction calculus it is used to "shorten" fractions.
This means that a common factor is removed from the numerator and denominator of a fraction, whereby the value of the fraction does not change. If you truncate a fraction with the greatest common divider of the numerator and denominator, you get a fraction that you cannot truncate any further, called a fully or maximally truncated fraction. A fraction is usually truncated in order to simplify further calculations with it.

How is the greatest common divider calculated?

For the calculation of the gcd there are 2 possibilities, on the one hand the prime factorization of both numbers and on the other hand over the so-called Euclidean algorithm. With the calculation by means of a prime factorization one takes the prime factors, which occur in both decompositions, and multiplies them with one another around the gcd to receive.
However, this process is very time-consuming, especially for large numbers, which is why a more efficient method, the so-called Euclidean algorithm, is used for such numbers. Here a division with remainder is carried out in successive steps, whereby the remainder becomes the new divider in the next step. The divider with the remainder 0 is the greatest common divider of both numbers.
Our online calculator uses the Euclidean algorithm to determine the gcd. Simply enter the two numbers whose gcd you want to determine and click on "Calculate".

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